Cone-beam CT (CBCT) with non-circular acquisition orbits has the potential to improve image quality, increase the field-of view, and facilitate minimal interference within an interventional imaging setting. Because time is of the essence in interventional imaging scenarios, rapid reconstruction methods are advantageous. Model-Based Iterative Reconstruction (MBIR) techniques implicitly handle arbitrary geometries; however, the computational burden for these approaches is particularly high. The aim of this work is to extend a previously proposed framework for fast reconstruction of non-circular CBCT trajectories. The pipeline combines a deconvolution operation on the backprojected measurements using an approximate, shift-invariant system response prior to processing with a Convolutional Neural Network (CNN). We trained and evaluated the CNN for this approach using 1800 randomized arbitrary orbits. Noisy projection data were formed from 1000 procedurally generated tetrahedral phantoms as well as anthropomorphic data in the form of 800 CT and CBCT images from the Lung Image Database Consortium Image Collection (LIDC). Using this proposed reconstruction pipeline, computation time was reduced by 90% as compared to MBIR with only minor differences in performance. Quantitative comparisons of nRMSE, FSIM and SSIM are reported. Performance was consistent for projection data simulated with acquisition orbits the network has not previously been trained on. These results suggest the potential for fast processing of arbitrary CBCT trajectory data with reconstruction times that are clinically relevant and applicable - facilitating the application of non-circular orbits in CT image-guided interventions and intraoperative imaging.